From the past, there is known a hydraulic shovel provided with a position detection device which detects the current position of a working point of a work implement. For example, in the hydraulic shovel disclosed in Japanese Unexamined Patent Application Publication No. 2002-181538, position coordinates of a cutting edge of a bucket are computed based on position information from a GPS antenna. Specifically, position coordinates of the cutting edge of the bucket are computed based on parameters such as a positional relationship of the GPS antenna and a boom pin, lengths of each of a boom, an arm, and the bucket, and each of the direction angles of the boom, the arm, and the bucket.